3 papers
math.AT2026
Higher categories of bordisms with geometric structures
Daniel Grady, Dmitri Pavlov
We introduce a system of axioms that uniquely defines an (infinity,d)-category of bordisms equipped with geometric data. The underlying manifolds of these bordisms may be smooth, c…
math.AT2025
Classifying spaces of infinity-sheaves
Daniel Berwick-Evans, Pedro Boavida de Brito, Dmitri Pavlov
We prove that the set of concordance classes of sections of an infinity-sheaf on a manifold is representable, extending a theorem of Madsen and Weiss. This is reminiscent of an h-p…
math.AT2025
Combinatorial model categories are equivalent to presentable quasicategories
Dmitri Pavlov
We establish a Dwyer-Kan equivalence of relative categories of combinatorial model categories, presentable quasicategories, and other models for locally presentable (infinity,1)-ca…